The conventional wisdom going into the government shutdown was that cratering public opinion, combined with a significant economic pinch, would quickly force Republicans to abandon their scheme to destroy ObamaCare and to pass a clean budget. All President Obama would have to do is sit on his hands and watch the GOP eat itself.

Indeed, some commentators, like Ezra Klein at The Washington Post, said it was better for the government to shut down now, so that Republicans would get their comeuppance before Congress ran up against a far more worrisome fiscal deadline: The debt ceiling.

But despite the fact that polls indeed show that a majority of Americans are against them, it appears Republicans have other ideas.

Congress has until October 17 to raise the Treasury's borrowing limit or send the economy hurtling off on an uncertain, though likely calamitous, course. With the deadline looming ever closer, and with Republican hard-liners still unwilling to give on the budget, they are now eyeing plans to roll the two fights into one.

The GOP leadership has "nearly given up on the idea that Senate Majority Leader Harry Reid [D-Nev.] will concede anything" on the budget, according to National Review's Robert Costa. But they believe introducing the debt ceiling into the equation could "force Reid's hand."

Rep. Paul Ryan (R-Wis.), the House GOP's budget chairman, predicted last week that this would happen. "I think that's inevitable, and preferable in my opinion," he told National Review. "I like combining all of our leverage, which is sequester and the debt limit."

While digging in on the debt ceiling would represent a major escalation, and put the economy at risk of another recession, Republicans believe it will place them on more politically favorable ground.

With the debt ceiling, Republicans could frame the debate around their desire to cut spending, something more understandable to a wider swath of voters. And while Democrats have almost uniformly opposed the GOP's demands thus far, Republicans feel the debt ceiling's more dangerous implications could spook enough Democrats — including Obama — to go weak at the knees. After all, Democrats accepted the sequester cuts to avoid crashing through the debt ceiling in 2011.

However, there's one snag in the GOP's budding plan: Democrats, too, think the debt ceiling is their fight to lose.

For Democrats, the thinking is simple. The GOP appears to be losing the shutdown argument, and hard. Given how poorly that has played out, "it's hard to imagine Republicans turning around the next day and forcing default," says Bloomberg Businessweek's Joshua Green.

A CNN poll Wednesday found that a majority of Americans thought a debt default would be terrible, while 53 percent said they would blame congressional Republicans should that happen. Only 31 percent pointed fingers at the president.

Further, big business interests, squeamish about a potential default, are already calling on Republicans to drop their demands. The U.S. Chamber of Commerce — which spent millions in the last election cycle against Democratic candidates — signed a letter Monday with 251 allied groups calling on Congress to "expeditiously" fund the government and raise the debt ceiling without tying either to extraneous demands.

Obama has flatly said that he will not negotiate on the debt ceiling. And he has an incentive not to cave, since doing so "makes an eventual breach inevitable," says Slate's Matthew Yglesias, by proving that the "hostage-taking gambit works."

The main concern for Democrats would be if the public, over time, begins to blame Obama for the standoff as well. Oh, and the whole sending the global economy into a tailspin thing.